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Revista Facultad de Ingeniería Universidad de
Antioquia
ISSN: 0120-6230
[email protected]
Universidad de Antioquia
Colombia
González-Morales, Luis Gerardo; Colina-Morles, Eliezer; Vanegas- Peralta, Pablo; SemperteguiÁlvarez, Rodrigo Efraín
Electrical energy conversion system design with single-phase inverter and H5 transformerless topology
Revista Facultad de Ingeniería Universidad de Antioquia, núm. 73, diciembre, 2014, pp. 79-89
Universidad de Antioquia
Medellín, Colombia
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Rev. Fac. Ing. Univ. Antioquia N. º73 pp. 79-89, December, 2014
Electrical energy conversion system design with
single-phase inverter and H5 transformerless
topology
Diseño de un sistema de conversión de energía
eléctrica con un inversor monofásico con
topología H5 sin transformador
Luis Gerardo González-Morales1,3*, Eliezer Colina-Morles1,2, Pablo VanegasPeralta2, Rodrigo Efraín Sempertegui-Álvarez3
Departamento de Electrónica y Comunicaciones, Universidad de los Andes.
Núcleo la Hechicera. C.P. 5101. Mérida, Venezuela.
1
Departamento de Ciencias de la Computación, Universidad de Cuenca. Av.
12 de Abril, ciudadela universitaria. C.P. 010150. Cuenca, Ecuador.
2
Departamento de Eléctrica, Electrónica y Telecomunicaciones, Universidad
de Cuenca. Av. 12 de Abril, ciudadela universitaria. C.P. 010150. Cuenca,
Ecuador.
3
(Received March 04, 2014; accepted July 21, 2014)
Abstract
This paper presents the design of an electrical energy conversion system
(EECS) for the use of solar energy and its conditioning for injection of
energy to the commercial power grid. A single-phase full-bridge inverter with
transformerless H5 topology coupled to an LCL filter is used. The system is
identified using an averaged small-signal state space model; while the used
cascade control scheme is tuned by pole placement and includes a maximum
power disturb-observe tracking type algorithm of that increases efficiency
by operating the system at the optimum operating point of the solar panel.
This design describes essential technical aspects in the components sizing
and selection for experimental development, as well as the control structure
design for a good performance to face systems perturbations.
----------Keywords: single-phase inverter H5, solar energy, control
systems, Unipolar PWM
Corresponding author: Luis Gerardo González Morales, e-mail: [email protected]
*
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Rev. Fac. Ing. Univ. Antioquia N.° 73. December 2014
Resumen
Este artículo presenta el diseño de un sistema de conversión de energía eléctrica
(SCEE) para el aprovechamiento de energía solar y luego acondicionamiento
e inyección de energía a la red eléctrica comercial. Se utiliza un inversor
puente completo monofásico con la topología sin transformador H5 acoplado
a un filtro LCL. El sistema es identificado mediante el modelo de estado
promediado y de pequeña señal, el esquema de control presenta un control
en cascada sintonizado mediante la asignación de polos, además de un
algoritmo de seguimiento de máxima potencia de tipo perturbar y observar
que permite aumentar la eficiencia del sistema, operando en el punto óptimo
de funcionamiento del panel solar. En el diseño se describen aspectos técnicos
fundamentales en el dimensionamiento y selección de componentes para su
desarrollo experimental, así como el diseño de la estructura de control para un
buen desempeño ante perturbaciones del sistema.
----------Palabras clave: inversor monofásico H5, energía solar, sistema
de control, modulación unipolar PWM
Introduction
Due to the high fossil fuels’ costs and the various
international agreements among industrialized
countries to reduce CO2 emissions, the use of
renewable energy has increased in recent decades.
In particular, systems for converting solar energy
are considered the most viable alternatives
amongst renewable energy technologies, which
have been adopted throughout the world to
meet the basic needs of electricity, particularly
in difficult access remote areas [1]. For solar
photovoltaic systems, the captured energy
requires of electronic systems called power
converters to adapt the initial current to the needs
of its load [2]. Traditionally, this load is associated
with AC through the commercial power grid, but
can also be fitted for a DC bus in accordance with
the new trends in micro and smart grid networks
[3, 4]. In EECS from renewable sources, energy
management is generally carried out by power
converters. Efficiency and cost are important
elements for selecting a particular topology.
When inverters are connected to the network,
it is common to use isolation transformers
between the power converter and the grid. Often,
these low frequency transformers are large
in volume, weight and price, which make the
80
converter unfeasible. In order to cope with this
problem, a number of low power alternatives
as transformerless topologies, have been
suggested in the literature [5]. Using grid tied
inverters without galvanic isolation between the
solar panels and the grid can bring some major
problems in their operation, as the common
mode voltage and high leakage currents through
the solar panels and installation. These problems
may be caused by conditions such as humidity
or even the way to setup [6]. The topology used
in this work corresponds to the full-bridge or
four switches H-bridge plus a fifth switch, hence
the name H5. The technique developed by [7] is
currently used by one of the largest worldwide
inverters manufacturers as it is SMA. The
topology is based on the full bridge and unipolar
pulse-width modulation (PWM) technique.
This technique allows a switched output current
whose low frequency component is obtained by
a third order LCL filter, which is dimensioned so
as not posing a significant reduction in efficiency.
This work proposes a cascade control structure
that allows delivering electricity to the grid in
compliance with known technical specifications
and takes into account the increased use of energy
supplied by solar panels.
Electrical energy conversion system design with single-phase inverter and H5 transformerless topology
Dimensioning of the power
converter
The principle of operation of the H5 topology is
based on the full-bridge inverter with a fifth switch
that separates the solar panel power converter, as
shown in figure 1. This topology is based on the use
of the unipolar PWM modulation which allows,
under the condition of zero voltage on the load of
the unipolar modulation, opening the switch S5.
The zero-voltage states are met when there is flow
through switch S1 and the freewheeling diode of
switch S3, or when there is circulation via switch
S4 and diode of switch S2; both combinations only
for the positive half cycle of the output current of
the inverter. Similarly, for the negative half cycle
combinations are: S2 when there is flow both in the
S2 switch and the freewheeling diode of S4 or when
there is circulation through switch S3 and diode
of S1. If switch S5 is open, the generation stage
is isolated from the converter and common mode
voltages as well as leakage currents are reduced.
Figure 2 shows the logical scheme of driving the
switch S5 on the basis of the full bridge switches.
A crucial aspect in the H5 topology is a suitable
selection of S5 switch; as its performance can be
affected by conduction losses of S5. This topology
allows operating in two quadrants with a reduced
number of components and a moderate yield.
It also allows for a simple control structure with
good performance against disturbances at the point
of rated power. The full bridge inverter requires
a configuration of anti-parallel diodes for each
switch in order to allow conducting when inductive
loads are presented. This case of study considers
powers up to 1.5KW, so it is possible to use Mosfet
transistors at 15 kHz switching frequency.
Figure 1 Full bridge inverter H5 and LCL filter scheme
Figure 2 Logical switching scheme for switch S5
Solar panel model
One of the most important aspects in the design of
the system shown in figure 1 is to specify the power
and voltage of the solar array input panels. In this
case, a set of 8 solar panels in series modeled with
the features of SLK60P6L at 220W have been
used. For maximum power, the equivalent solar
panel can be modeled as shown in figure 3, where
the point of maximum power output of the panel
assembly is defined by Ppv_mppt = 1600W @
(Vpv_mppt = 200V, Ipv_mppt = 8.07A).
Figure 3 Equivalent power vs. voltage characteristic
of the solar panel for different radiations @ T = 25 °C
Dimensioning the LCL filter
It is common to couple output filters to full-bridge
inverter to reduce the high frequency components
(harmonics) in the voltage and load current. In
particular, in cases where low power converters
inject power into the grid, it is necessary to
comply with the standard for harmonic emissions
IEC 61000-3-2, which applies to equipment
connected to the grid with currents lower than
16A per phase. In this work the LCL filter type
[8], with a dimensioning method that depends
on the desired attenuation in the frequency
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Rev. Fac. Ing. Univ. Antioquia N.° 73. December 2014
range, is used. Specifically, the LCL filter has an
-60db/decade output current attenuation from its
resonance frequency and thus low consumption of
reactive power. The procedure for dimensioning
the components of the LCL filter is presented
in [8], where the current and impedance are
determined based upon the nominal power value​​
of S0 = 1500W and voltage V0 = 120V, equations
(1) and (2).
I0=
Z0=
So
Vo
Vo
Io
=12.5 A
=9.6 Ω
(1)
(2)
Once the system current and base impedance
are known, the current consumption of the filter
capacitor C is lowered to less than 5% of the
rated current of the system to limit the power
consumption, as shown in equation (3).
IC=0.05 ∙Io=0.625 A(3)
Once known the capacitor current, the capacitive
reactance and the capacitance C are determined
by equations (4) and (5), at the network frequency
fg = 60Hz.
Xc=
C=
1
ω1 Xc
Vo
IC
=192 Ω
=13.81μF, conω1=2 π fg
(4)
(5)
To calculate the inductor L, the criterion is to
determine the maximum voltage drop across the
inductor under nominal conditions. In this case,
the inductive reactance XL is fixed to less than
5% of the base impedance (equation 6), and the
inductance L is calculated using equation (7).
XL=0.05∙Zo=0.48Ω
L=
82
XL
ω1
=192 Ω
(6)
(7)
For inductance Lg is necessary to define the
resonance frequency. It is common to center it
within the range defined in equation (8), which
depends on the frequency of the network fg and
the switching frequency fsw used by the converter.
10∙f_g<f_resonance</2
fsw
2
(8)
With this approach it is possible to reduce
the switching harmonics located at twice the
switching frequency and its multiples (2 ∙ n ∙ fsw).
Equation (9) relates the resonant frequency of the
filter and its components:
(9)
From equation (8), the resonance frequency
fresonance= 4050Hz is fixed and through equation (9)
the inductance Lg=0.11mH. Another important
factor in dimensioning the filter is the damping
resistor Rd, which aids to limit the high gain of
the filter at the resonant frequency. This damping
resistor is calculated by studying its effect on the
control loop, as presented later.
Dimensioning the capacitor “DC-link”
Within the required components in the system
design, it is necessary to use a capacitor Cdc,
commonly called “DC-link” capacitor which
allows to significantly reduce the oscillations of
the voltage at the inverter input and the variations
around the operating point of the solar panel.
A DC-link capacitor thereby contributes to
increasing the system performance and performs
well with stable dynamics in the control system.
One of the criteria used for dimensioning the
DC-link capacitor is to limit fluctuations to 5%
of the voltage at the panel maximum power point
ΔVpv_mppt=0.05∙Vpv_mppt. The relationship that
limits ΔVpv_mppt voltage variations as function of
the rated power Ppv_mppt, fg frequency network and
capacitance Cdc, is given by equation (10), and
yields Cdc = 2.6mF.
Electrical energy conversion system design with single-phase inverter and H5 transformerless topology
∆Vpv_mppt=
Ppv_mppt
2∙fg∙Cdc∙Vpv_mppt
(10)
Once the capacitance of the DC-Link capacitor is
known, it is necessary to determine the maximum
rms current at “rated power”. This is because
along with the operating temperature are the
elements that significantly reduce its usage time
[9]. Equation (11), used in [10], determines the
current ic_dc rms of the capacitor Cdc as function
of the modulation index d, peak output current
of the inverter îL and phase angle between the
voltage and current output φ.
4 corresponds to the model of the considered
circuit.
(13)
(14)
(15)
(11)
A rated power, the maximum current to circulate
through the condenser Cdc is ic_dc = 6.07A.
Figure 4 Small signal model for the power conversion
system
Modeling and control system
From the small signal model shown in figure
4, the transfer function of the voltage versus
modulation index is obtained in equation (16).
Assuming that variations in the input voltage are
negligible allows for a SISO type control system.
Small signal model
In this part the dynamics of the power converter,
the LCL filter and control system are studied.
Firstly, the development of a small-signal model
for the single-phase inverter is derived from a
Buck converter [11] and starts from the average
state model equation (12).
vab=(2d-1)∙vpv(12)
Where d is the amplitude modulation index,
which relates the amplitude of the control signal
and typical PWM modulation carrier signal [12].
From equation (12) a first order linearization
is performed and set as criterion that variables
expressed in lowercase, under the symbol “~”,
correspond to small-signal model variables and
uppercase variables express the steady state
operation. Thus, equation (13) expresses the
equivalent model of the voltage in the power
converter in steady state, while the small-signal
model for the voltage and current is defined by
equations (14) and (15) respectively. Figure
(16)
Equation (17) shows the transfer function of the
LCL filter used. This equation, together with
equation (16) determines the overall transfer
function of the process being controlled.
(17)
with
Figure 5 shows the frequency responses of
the LCL filter for different values of Rd = [0,
3, 5, 10] Ω. It can be observed a significant
increase in gain due to the resonance of the filter
(fresonance=4050Hz) when Rd=0Ω, which may
cause serious problems in the performance of
the control system. To solve this problem, it is
proposed to incorporate the damping resistor Rd
so significantly attenuates the gain at fresonance. The
83
Rev. Fac. Ing. Univ. Antioquia N.° 73. December 2014
graph shows that as Rd increases, the filter gain
does not vary significantly, but for frequencies
near the resonance, it is attenuated completely.
Importantly, as Rd increases the filter gain is
reduced as well as the efficiency of the system.
Figure 6 Double update PWM Modulator
Figure 5 Bode diagram LCL filter
Current control loop
In relation to the control strategy, the average
current control (ACC) technique is considered
[13, 14], which allows using the average state
model to half the switching frequency, so that the
speed response of the control loops involved is
connected with this condition. Once identified the
control strategy is necessary to define the type of
modulator. In this case, the unipolar modulation
is used, which is a necessary condition for the H5
topology. This technique reduces the harmonic
current injected to the network, especially in
cases when the modulation index is low [15, 16].
Another advantage of the unipolar modulation
technique consists in the considerable reduction
of the rms current of the capacitor Ccd.
Equation (18) represents the transfer function
of the modulator used in this application and
corresponds to the double update PWM studied in
[17], where the output signals to the comparator
modulator are updated only when the carrier
signal value reached minimum and maximum, as
can be seen in figure 6.
84
(18)
This transfer function is dependent on the peak
to peak amplitude of the triangular comparison
signal Vpp=1 of the duty cycle D, which in this
case is considered as an average value of a
switching cycle (D = 0.5), and the maximum time
delay expressed as Ts=0.5Tsw.
In order to facilitate the study of the control
loops in continuous time, and in turn introduce
the effects of the delay resulting from the digital
sampling into the temporal analysis, the second
order Pade approximation given in (19) [18] has
been used in the transfer function (18).
(19)
Figure 7 illustrates the block diagram of the
proposed control system after modeling the
elements of the energy conversion system. This
diagram has a cascade control, where the inner
loop controls the output current of the LCL filter
in terms of the modulation index amplitude d.
The outer control loop is used to regulate the
voltage of the panel. This control variable is
important because it is closely related to the
maximum power point of the solar panel. The
voltage control loop is responsible for setting
the amplitude of the reference current and with
the PLL synchronization algorithm provides a
sinusoidal reference current in phase with the
network voltage Vred. This algorithm is used
in [19] and is not part of interest of this work.
It is worth mentioning that within the control
system also operates a maximum power search
Electrical energy conversion system design with single-phase inverter and H5 transformerless topology
algorithm, responsible for setting the reference
voltage Vpv_ref for voltage control loop, which
will be discussed later.
Figure 7 Voltage and current control loop
For the stability analysis of the current control
loop, the open loop gain shown in equation (20)
is used.
rad/s determines the frequency of the desired
resonant gain [20]. Figure 8 illustrates the
behavior of the current control loop where the
frequency response is observed. In the case when
Rd=0Ω, the loop gain at the resonance frequency
is high, jeopardizing the stability of the system,
reason why the inclusion of the damping resistor
Rd=3Ω and the proportional control is suggested.
With this control the frequency response is stable.
The contribution of the resonant control ensures
that the output current present less distortion, the
proposed controller has a PM= 56.6 °, a GM=11db
and a zero crossing frequency fTi_crossing=637Hz, so
the system stability is guaranteed.
Ti=Gci_inv∙Gpwm∙Gi_inv ∙Gf_lcl ∙βi(20)
Where βi is the gain of the current sensor, which
in this application βi=1.
Regarding the Gci_inv function, which corresponds
to the controller, the proportional plus resonant
type formulated in (21) has been selected, which
allows tracking the reference current in addition
to introducing a control loop gain at the network
frequency that improves the distortion of the
injected current for frequencies near fg. For
tuning the controller parameters, the value of kp
was selected using pole placement technique.
This technique allows to determine the controller
gain kp such that bode diagram of the open-loop
gain Ti exhibits a very similar dynamics to a pure
integrator “1/s”, with a gain margin GM > 6db
and a phase margin MF > 50 °, if the zero crossing
frequency is lower than half of the switching
frequency (frequency where the average states
model becomes invalid). A value of kp = 0.05 is
obtained by applying the methodology described
above.
(21)
In relation to the resonant control parameters,
these have been tuned as follows: kh=5 is the
gain of the resonant peak, Bh=4∙π rad/s is the
bandwidth of the resonant peak and ωh=2∙π∙60
Figure 8 Frequency response of the current loop Ti
Voltage control loop
Once the response speed of the current control
loop for zero crossing frequency is set, the voltage
transfer function is determined using equation
for
(22). This function is valid assuming
frequencies below the zero crossover frequency
of the loop current control.
(22)
The loop gain for the voltage regulation vpv is
given by equation (23), where it was considered
that the gain of the sensor voltage is βv=1.
(23)
85
Rev. Fac. Ing. Univ. Antioquia N.° 73. December 2014
Given its characteristic, the transfer function for
Gv_inv corresponds to PI controller shown in equation
(24).
(24)
The voltage controller tuning is performed,
as in the current control by pole assignment at
zero crossover frequency near 63.7Hz. This
frequency is located a decade below to the
response of the current loop, although this
frequency might include dynamics affecting
the harmonic distortion in the current reference
of the inner loop, so it is suggested to decrease
it according to the commitment efficiency vs.
harmonic distortion permitted by the system.
With these assumptions, the values of Kpv and
Ki are obtained as 0.4 and 24, respectively. The
frequency response of the voltage control loop is
depicted in figure 9, showing a stable behavior
with an MG = 36db and an MF = 79.6°.
simplicity, perturb & observe technique P&O
[21] is one of the most widely used, because it
is not necessary to know the model of the energy
conversion system. In this case, the algorithm
defines the reference voltage Vpv_ref shown in
figure 7. For tuning the algorithm a stabilization
time ts=25ms and step size ΔVref=1V are used.
Performance of the power
conversion system
Once the solar energy conversion system using
the parameters shown in table 1 and the power
electronic circuits Psim® 7.0 simulation software is
designed, it is possible to observe the behavior of the
system to a disturbance in the solar incidence with
200W/m2 steps, starting in 200W/m2 and ending at
1000W/m2. Figure 10 includes the behavior of the
current loop in the inverter. It is possible to observe
the increase of the current delivered to the network
in proportion to the increase in solar radiation
incidence. Likewise is noted that the current
regulator allows the current to follow the reference
controlled with stable dynamics.
Table 1 Specifications design and circuit parameters
Description
Ppv_max
fsw
fg
L
Lg
Rd
C
Cdc
Vo
Value
1600 W.
15kHz
60Hz
5.26mH
0.11mH
3Ω
13.81μF
2.6mF
120V rms
Figure 9 Frequency response of the voltage loop Tv
Tracking maximum power point
algorithm (MPPT)
Since the maximum efficiency point of the solar
panel varies depending on the solar radiation and
has non-linear dynamic behavior, it is necessary to
use a maximum power tracking algorithm. There
are several types of this technique, but due to its
86
Figure 10 Output current behavior Ig to different
solar radiation steps
Electrical energy conversion system design with single-phase inverter and H5 transformerless topology
Figure 11a is an enlargement of figure 10, which
shows that for a solar irradiation of 200W/m2 an
output current with an amplitude of Ig=2.9A rms
and distortion near THDi<5% is obtained. Figure
11b illustrates the behavior of the output current
at nominal power. If solar irradiation were
1000W/m2, would have an amplitude of Ig=13.5A
rms and THDi<2%, enabling compliance with
the IEC 61000-3-2 standard, which relates the
harmonic distortion to equipment connected to
the network.
Figure 12 shows the voltage loop behavior which
chatters around the reference voltage set by the
MPPT algorithm. Ripple is closed to the fixed
by capacitor Cdc. The same figure shows that
the output current Ipv of the solar panel increases
proportionally to the power Ppv handled by the
system.
Figure 12 Behavior of the control loop voltage and
MPPT algorithm
Figure 13 shows the performance of the
maximum power tracking algorithm MPPT. Due
to its oscillating nature, this algorithm operates
around the maximum power point for each case
of solar irradiation.
a)
Figure 13 Performance of the maximum power
tracking algorithm MPPT
Conclusions
b)
Figure 11 Enlargement of figure 10. Output current Ig
This paper has considered a solar energy
conversion system that consists of a full-bridge
inverter with transformerless H5 topology
87
Rev. Fac. Ing. Univ. Antioquia N.° 73. December 2014
coupled to a LCL filter. The advantage of this
topology is to reduce common mode currents
isolating the inverter from the solar panel by
means of an additional switch instead of the
classic full-bridge inverter. The control scheme
contains a cascade control and a maximum
power tracking algorithm operating near the
maximum performance point, which allows
power delivery to the grid with low distortion.
The presented design is a viable solution for
low power applications, since it is possible to
remove isolation by low frequency transformers,
which in most cases increases the cost and size of
inverters. Dynamic performance under varying
solar incidence has been stable and the results
have been verified by computer simulation with
the simulation software Psim® 7.0
Acknowledgments
This work was sponsored by Prometeo
Project, promoted by the Secretariat of Higher
Education, Science, Technology and Innovation,
SENESCYT, Ecuador.
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